Question
The harmonic mean of two numbers is 4, their A.M. A, and G.M. G, satisfy the relation 2A + G^{2} = 27. Find the two numbers.

2 and 3

6 and 3

5 and 4

None of these
medium
Solution
6 and 3
.
Also 2A + G^{2} = 27 or 2A + 4A = 27
From (i) and (ii) we conclude that a and b are the roots of
.
Hence the numbers are 6 and 3.
SIMILAR QUESTIONS
The fifth terms of an A.P. is 1 whereas its 31st term is – 77. Find its 20^{th} term and sum of its first fifteen terms. Also find which term of the series will be –17 and sum of how many terms will be 20.
The nth term of a series is given to be , find the sum of 105 terms of this series.
Find the sum of the first 24 terms of the A.P. a_{1}, a_{2}, a_{3}, … If it is known that .
…to n terms.
The third term of a G.P. is 4. The product of first five terms is
The A.M. between m and n the G.M. between a and b are each equal to (ma + nb)/(m + n). Find m and n in terms of a and b.
A.M. and H.M. between two quantities are 27 and 12 respectively, find their G.M.
The sum of three numbers in H.P. is 26 and sum of their reciprocals is 3/8. Find the numbers.
If x, y, z are in G.P.,
Balls are arranged in rows to form an equilateral triangle. The first row consists of one ball, the second row of two ball and so on. If 669 more balls are added then all the balls can be arranged in the shape of a square and each of the sides then contains 8 balls less than each side of the triangle did. Determine the initial members of balls.